P100 Preparatory Segment

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This publication is a useful tool for students in TTi's courses, both for preparation before their courses (to bone up on forgotten math, dynamics and electrical concepts) and for reference after their courses.

Mathematics topics include: Basic Math, Logarithms and Decibels, Algebra, Geometry, Trigonometry, Vectors and Phasors, Complex numbers and Calculus.

Dynamics topics include: Dynamic Force and Motion; Materials, Stress and Strain; Torque, Moments of Inertia, Beam theory and Fatigue.

Electrical topics include: Basic Electrical Theory, EMFsin Series and Parallel, Kirchhoff’s Laws, Thevenin's and Norton’s Theorems, Alternating Current –Series and Parallel, AC Circuits, Phasors, Complex, Non-Sinusoidal and Square Waveforms.

Course Outline

Chapter 1A - Review of Basic Mathematics

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• Mathematical Symbols
• Some math terminology
• Useful Conversions
• Computer/Calculator Convention for indicating decimal place
• Useful Constants
• Trigonometric Ratios
• Scientific Notation, with examples
• Engineering Notation, with examples
• Greek Letter Symbols

Chapter 1B - Logarithms and Decibels

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• Logarithms
• Laws of Common and Natural Logarithms
• Application of Logarithms to Decibel Ratios
• Decibels—Power Ratio
• Decibels—Voltage Ratio

Chapter 1C - Introduction to Algebra

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• Constants and Variables
• Introduction to Algebra
• Terms of an Equation
• Direct Proportionality
• Inverse Proportionality
• Solving Simple Equations
• Exponential Equations
• Simultaneous Linear Equations
• Definitions
• Squaring Binomials
• Factoring Method
• Perfect Square Method
• Completing the square
• Graphs
• Example: Linear Equation Graph
• Geometric Representation of an Equation

Chapter 1D - Review of Geometry/Introduction to Trigonometry

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• Review of Geometry
• Angles
• Arcs and Circles
• Conversions Between Degrees and Radians
• Degrees, Minutes, Seconds
• Angles, Chords
• Area of Sector
• Polygons
• Triangles
• Types of Triangles
• Pythagoras' Theorem
• Introduction to Trigonometry
• Complementary Functions
• Trigonometric Functions of Angles
• Spiral of Roots
• Applying Pythagoras' Theorem
• Graphing of Trigonometric Functions
• Trigonometry Reference

Chapter 1E - Vectors, Sine Waves, Phase

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• Vectors
• Vectors and Angular Velocity
• Linear and Angular Velocity
• Phase Difference
• Critical Functions
• Linear Coordinates of a Rotating Vector

Chapter 1F - Complex Algebra

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• Rectangular Coordinates of a Vector
• Polar Coordinates of a Vector
• Complex Algebra:
• Real and Imaginary Numbers
• Complex Numbers
• Vector in Complex Plane
• Converting from Rectangular to Polar Form
• Addition and Subtraction of Complex Numbers
• Multiplying Complex Numbers
• Rectangular Form
• Polar Form
• Division of Complex Numbers
• Rectangular Form
• Polar Form

Chapter 1G - Introduction to Calculus

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• Defining Calculus
• Differentiation
• Differential Equations
• Differentiation
• Examples
• Useful Rules
• Differentiating a Function Again
• Example of Curve DrawingRules for Curve Drawing
• Differentiating Trigonometric Functions
• Integration
• Area Under a Curve
• Integration Examples
• Rules of Integration
• Differential Equations

Chapter 2A - Dynamic Force and Motion

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• Laws of Motion
• Weight vs. Mass
• System of Units
• Conversion of lbm to lbf
• Slugs vs. Pounds Mass
• Common Units of Mass
• Weight, Mass and Gravity
• Specific Weight
• Relative Density and Specific Gravity
• Common Units of Force
• Definitions of Common Mechanical Terms
• Friction and Wear
• Work, Power
• Energy

Chapter 2B - Structural Theory: Materials, Stress, and Strain

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• Engineering Materials
• Jet Engine Component Examples
• Stress and Strain
• Definition of Stress
• Shear Stress and Tensile Stress
• 1) Simple Tension or Compression
• 2) Pure Shear
• Strain
• Shear Strain
• Elasticity—Definitions and Laws
• Stress-Strain Relationship
• Tensile Strength
• Non-linear Elastic and Anelastic Solid Material
• Non-Elastic (or Plastic) Load-Extension (F/δ) Curves
• Nominal Stress/Nominal Strain (σn / εn )

Chapter 2C - Structural Theory: Torque, Moments of Inertia

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• Torque (T)
• Tangential acceleration (at)
• The Mass Moment of Inertia (Im)
• The Area Moment of Inertia (IA)
• Relative Stiffness (k) of Structural Members
• Shearing Torques
• Twisting Torques
• Torsional Stiffness (kr)
• Torsional Shape Factor (J) Comparisons
• Moment of Inertia—Transfer Formula
• Parallel Axis Method
• Angular Transfer Method

Chapter 2D - Structural Theory: Beams

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• Simple Beam
• Bending Moment
• Elastic Deflection of a Simply Supported Beam
• Bending Strengths
• Structural Beams
• Bending Stiffness of a Beam Kb
• Cantilever Beam

Chapter 2E - Fatigue

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• Stress-Number Curve (S/N curve)
• “S-N” Curve from Fatigue Testing
• Idealized S-N Curve for Structural Materials
• Fatigue
• Fatigue-Crack-Growth Rate
• Fast Fracture
• Crack Propagation
• Fatigue Failure
• Exponential Failure Model

Chapter 3A - Electrical Fundamentals Review

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• Electrostatic Field and Potentials
• Electrical Charge
• Magnetism
• Visualizing a Magnetic Field
• Magnetic Poles
• Induced Magnetism
• Forces of Attraction
• Electromagnetism
• Magnetic Effect of an Electric Current
• Electromagnetic Force
• Conductors and Insulators
• Current
• Resistance
• Voltage
• Ohm’s Law

Chapter 3B - EMFs in Series and Parallel

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• EMFs in Series and Parallel
• Resistors
• Electrical Circuits
• Resistors in Electric Circuits
• Series Circuits
• Parallel Circuits
• Example
• Conductance (G)
• DC Series-Parallel Circuits

Chapter 3C - Kirchhoff’s Laws; Thevenin’s and Norton’s Theorems

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• Kirchhoff’s First Law
• Example of Kirchhoff’s First Law
• Kirchoff’s Second Law
• Thevenin’s Theorem
• Example
• Norton’s Theorem

Chapter 3D - Alternating Current — Series and Parallel

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• Alternating Current
• Direct Current vs. Alternating Current
• Sine Wave
• Understanding RMS
• Average (Mean) and rms Values of Current and Power
• Heating Effect (Power) During ½ Cycle
• Another Method of Illustrating rms Values
• Form Factor
• Combining rms Voltages
• Effective or RMS Value of Current and Power

Chapter 3E - AC Circuits, Phasors

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• AC Circuits
• Example
• AC—Current and Voltage
• Example
• Phasors
• Impedance
• General AC vectors
• Examples
• Summary

Chapter 3F - Complex, Non-Sinusoidal and Square Waveforms

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• Complex Waveform
• Harmonics